Cruz called Trump a “pathological liar” and a “narcissist” while speaking to reporters on Tuesday in Indiana.

In a live phone call on Fox And Friends Tuesday, Trump repeated the explosive allegation being made by The National Enquirer: "Ted Cruz Father Linked To JFK Assassination".

“His father was with Lee Harvey Oswald prior to Oswald's being — you know, shot. I mean, the whole thing is ridiculous,” Trump said. “What is this, right prior to his being shot, and nobody even brings it up. They don't even talk about that. That was reported, and nobody talks about it.”

“I mean, what was he doing — what was he doing with Lee Harvey Oswald shortly before the death? Before the shooting? It’s horrible,” Trump added.

Cruz blasted Trump's accusations and the report. He sarcastically said: "Yes, my dad killed JFK. He is secretly Elvis, and Jimmy Hoffa is buried in his backyard!"

The tabloid claims a photo of a man handing out pro-Cuba leaflets with Oswald in August 1963 -- three months before President Kennedy was assassinated, is Rafael Cruz, Ted's father.

The man in the photo has never been identified and The National Enquirer quoted one expert as saying he looks like Ted Cruz’s father as a young man.

"There’s more similarity than dissimilarity ... It looks to be the same person and I can say as much with a high degree of confidence,” the expert said.